To calculate the minimum, I would make a table with on each row: $\bot$, $A \bot$, $A^2 \bot$, ... and if there are two similar lines, that's our minimum. But once again I am not sure this is enough to do this.

Edit: This is the maximal fixpoint. The minimal fixpoint is $\bot$. There are two other fixpoints: $f(n) = 0$ for $n \leq 3$ and undefined otherwise, and $f(n) = 0$ for $n > 3$ and undefined otherwise.